id
int64 | question
string | final_answer
list | embedding
list |
|---|---|---|---|
800
|
A quarantined physics student decides to perform an experiment to land a small box of mass $m=60 \mathrm{~g}$ onto the center of a target a distance $\Delta d$ away. The student puts the box on a top of a frictionless ramp with height $h_{2}=0.5 \mathrm{~m}$ that is angled $\theta=30^{\circ}$ to the horizontal on a table that is $h_{1}=4 \mathrm{~m}$ above the floor. If the student pushes the spring with spring constant $k=6.5 \mathrm{~N} / \mathrm{m}$ down by $\Delta x=0.3 \mathrm{~m}$ compared to its rest length and lands the box exactly on the target, what is $\Delta d$ ? Answer in meters. You may assume friction is negligible.
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801
|
A wooden bus of mass $M=20,000 \mathrm{~kg}$ ( $M$ represents the mass excluding the wheels) is on a ramp with angle $30^{\circ}$. Each of the four wheels is composed of a ring of mass $\frac{M}{2}$ and radius $R=1 \mathrm{~m}$ and 6 evenly spaced spokes of mass $\frac{M}{6}$ and length $R$. All components of the truck have a uniform density. Find the acceleration of the bus down the ramp assuming that it rolls without slipping.
Answer in $\mathrm{m} / \mathrm{s}^{2}$.
<image_1>
|
[
"3.32"
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804
| "A ball is situated at the midpoint of the bottom of a rectangular ditch with width $1 \\mathrm{~m}$(...TRUNCATED)
|
[
"2"
] | [0.0172119140625,-0.004913330078125,-0.01708984375,0.03515625,-0.0011138916015625,0.01385498046875,0(...TRUNCATED)
|
805
| "A frictionless track contains a loop of radius $R=0.5 \\mathrm{~m}$. Situated on top of the track l(...TRUNCATED)
|
[
"$2.37$"
] | [0.038330078125,-0.0284423828125,-0.0113525390625,0.0274658203125,-0.005096435546875,0.046142578125,(...TRUNCATED)
|
809
| "The following diagram depicts a single wire that is bent into the shape below. The circuit is place(...TRUNCATED)
|
[
"$1.9$"
] | [0.0233154296875,-0.0166015625,-0.01373291015625,-0.0017242431640625,-0.01275634765625,0.00132751464(...TRUNCATED)
|
815
| "For his art project, Weishaupt cut out $N=20$ wooden equilateral triangular blocks with a side leng(...TRUNCATED)
|
[
"21"
] | [0.0262451171875,0.007415771484375,0.01092529296875,-0.01251220703125,-0.00433349609375,0.0070800781(...TRUNCATED)
|
818
| "The graph provided plots the $y$-component of the velocity against the $x$-component of the velocit(...TRUNCATED)
|
[
"1"
] | [0.0294189453125,-0.016845703125,-0.0201416015625,0.0238037109375,0.0003871917724609375,0.0358886718(...TRUNCATED)
|
820
| "While exploring outer space, Darth Vader comes upon a purely reflective spherical planet with radiu(...TRUNCATED)
|
[
"$1.33 \\cdot 10^{35}$"
] | [0.00299072265625,-0.01385498046875,0.0010833740234375,-0.0255126953125,0.01153564453125,0.019287109(...TRUNCATED)
|
822
| "Mario is racing with Wario on Moo Moo Meadows when a goomba, ready to avenge all of his friends' de(...TRUNCATED)
|
[
"40"
] | [0.035400390625,0.005218505859375,-0.0201416015625,-0.01361083984375,0.0205078125,0.019775390625,0.0(...TRUNCATED)
|
824
| "An engineer has access to a tetrahedron building block with side length $\\ell=10 \\mathrm{~cm}$. T(...TRUNCATED)
|
[
"4.62"
] | [0.0361328125,-0.005889892578125,-0.0185546875,-0.01336669921875,0.00946044921875,0.01446533203125,0(...TRUNCATED)
|
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